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For the Cos(2x)-Potential the coefficients of the weak- and strong coupling perturbation series of the ground state energy are constructed recursively. They match the well-known expansion coefficients of the Mathieu equation's…
We review briefly the fundamental equations of a semi-microscopic core-particle coupling method that makes no reference to an intrinsic system of coordinates. We then demonstrate how an intrinsic system can be introduced in the strong…
Graph-based approximation methods are of growing interest in many areas, including transportation, biological and chemical networks, financial models, image processing, network flows, and more. In these applications, often a basis for the…
In recent work we have shown that the Fermi liquid aspects of the strong coupling fixed point of the s-d and Anderson models can brought out more clearly by interpreting the fixed point as a renormalized Anderson model, characterized by a…
The recently established generalized Gell-Mann--Low theorem is applied in lowest perturbative order to bound-state calculations in a simple scalar field theory with cubic couplings. The approach via the generalized Gell-Mann--Low Theorem…
Graph neural networks (GNNs) are effective machine learning models for many graph-related applications. Despite their empirical success, many research efforts focus on the theoretical limitations of GNNs, i.e., the GNNs expressive power.…
We examine the large-order behaviour of a recently proposed renormalization-group-improved expansion of the Adler function in perturbative QCD, which sums in an analytically closed form the leading logarithms accessible from…
Weak measurement is a novel technique for parameter estimation with higher precision. In this paper we develop a general theory for the parameter estimation based on weak measurement technique with arbitrary postselection. The previous weak…
The weak coupling asymptotics to order $\gamma$ of the ground state energy of the delta-function Fermi gas, derived heuristically in the literature, is here made rigorous. Further asymptotics are in principle computable. The analysis…
The method of extrapolating asymptotic series, based on the Self-Similar Approximation Theory, is developed. Several important questions are answered, which makes the foundation of the method unambiguous and its application straightforward.…
For applications in chemistry and physics, machine learning (ML) is generally used to solve one of three problems: interpolation, classification or clustering. These problems use information about physical systems in a certain range of…
We calculate the effective action of a superconductor, without assuming that either the electron-electron potential or the Fermi surface obey rotational invariance. This approach leads to the same gap equation and equilibrium free energy as…
What should a function that extrapolates beyond known input/output examples look like? This is a tricky question to answer in general, as any function matching the outputs on those examples can in principle be a correct extrapolant. We…
Much of interesting complex biological behaviour arises from collective properties. Important information about collective behaviour lies in the time and space structure of fluctuations around average properties, and two-point correlation…
Extreme value theory provides rigorous theory and statistical tools for extrapolation in machine learning, particularly in settings where traditional methods struggle due to data scarcity in the tails. A broad range of tasks benefit from…
Power-suppressed corrections coming from the end-point integration regions in the amplitude of the process $\gamma^{*}\gamma \to \pi \pi$ at large $Q^2$ and small squared center-of-mass energy $W^2$ are calculated in the QCD hard-scattering…
A systematic derivation provides extended series of correlation inequalities in quantum systems. Each order in truncated Taylor expansion of the spectral representation for the Duhamel correlation function gives its lower and upper bounds.…
The weak value amplification technique has been proved useful for precision metrology in both theory and experiment. To explore the ultimate performance of weak value amplification for multi-parameter estimation, we investigate a general…
We extend the idea of weak measurements to the general case, provide a complete treatment and obtain results for both the regime when the pre-selected and post-selected states (PPS) are almost orthogonal and the regime when they are exactly…
We propose new compressive parameter estimation algorithms that make use of polar interpolation to improve the estimator precision. Our work extends previous approaches involving polar interpolation for compressive parameter estimation in…